What is "power law"

n. (context mathematics English) A mathematical relationship in which the magnitude of something is proportional to a fixed power of the magnitude of something else (i.e. the relationship takes the form ''f''(''x'') = ''a.x^k''). (from 20th c.)

n. (psychophysics) the concept that the magnitude of a subjective sensation increases proportional to a power of the stimulus intensity [syn: Stevens' law, Stevens' power law]

In statistics, a power law is a functional relationship between two quantities, where a relative change in one quantity results in a proportional relative change in the other quantity, independent of the initial size of those quantities: one quantity varies as a power of another. For instance, considering the area of a square in terms of the length of its side, if the length is doubled, the area is multiplied by a factor of four.